Nonsense, it's run by fallible humans.
People very often get two words mixed up here.
Infallible —
and Impeccable.
We are all impeccable....we can all make a mistake.
Through the Holy Spirit, much prayer, determination, proof, etc. a doctrine or dogma is pronounced infalliable — note the entrance of the Holy Spirit in this process.
In other words, your assertion could be wrong ;-)
oh, the popes are fallible allright, but Christ promised that in matters of faith and morals, they would never teach in error.....does that mean that they could not sin on their own...of course not, but in matters pertaining to official teachings, they would be protected from error.
so far it has worked just fine!!!!